Almost and nearly basically differ on how you use them, because the meaning is practically the same.
There are sentences in which both can be used, such as:
It's almost/nearly time to go to bed, almost/nearly all my friends will be there.
Neraly, however, is not used for negative sentences, so when saying things like "Almost nobody was there / she's almost never on time" we use almost. (With never, no, anything, nothing, nobody...)